Revolutions in Mathematics
by Gillies, DonaldEdition: Reprint
Format: Paperback
Pub. Date: 1995-12-14
Publisher(s): Clarendon Press
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Summary
The essays in this book provide the first comprehensive treatment of the concept of revolution in mathematics. In 1962 an exciting discussion of revolutions in the natural sciences was prompted by the publication of Kuhn's The Structure of Scientific Revolutions. A fascinating but little knownoffshoot of this debate was begun in the USA in the mid-1970s: can the concept of revolutions be applied to mathematics as well as science? Michael Crowe declared that revolutions never occur in mathematics, while Joseph Dauben argued that there have been mathematical revolutions and gave someexamples.The original papers of Crowe, Dauben, and Mehrtens are reprinted in this book, together with additional chapters giving their current views. To this are added new contributions from nine further experts in the history of mathematics who each discuss an important episode and consider whether it was arevolution.This book is an excellent reference work and an ideal course text for both graduate and undergraduate courses in the history and philosophy of science and mathematics.
Table of Contents
| Preface | |
| Introduction | |
| Ten 'laws' concerning patterns of change in the history of mathematics 1975 | |
| T.S. Kuhn's theories and mathematics: a discussion paper on the new historiography of mathematics 1976 | |
| Appendix 1992 revolutions reconsidered | |
| Conceptual revolutions and the history of mathematics: two studies in the growth of knowledge 1984 | |
| Appendix 1992: revolutions revisited | |
| Descartes's geometrie and revolutions in mathematics | |
| Was Leibniz a mathematical revolutionary? | |
| The 'fine structure' of mathematical revolutions: metaphysics, legitimacy, and rigourGiulio Giorello | |
| The case of calculus from Newton to Berkeley and MacLaurin | |
| Non-Euclidean geometry and revolutions in mathematics | |
| The 'revolution' in the geometrical vision of space in the nineteenth century, and the hermeneutical epistemology of mathematics | |
| Meta-level revolutions in mathematics | |
| The nineteenth-century revolution in mathematical ontology | |
| A restoration that failed: Paul Finsler's theory of sets | |
| The Fregean revolution in logic | |
| Afterword 1992 | |
| A revolution in the historiography of mathematics? | |
| About the contributors | |
| Bibliography | |
| Index | |
| Table of Contents provided by Publisher. All Rights Reserved. |
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